20+ Expert’s Sharing Tips on Picking the Ideal Math Tutor
20+ Expert’s sharing tips on picking the ideal math tutor
Edward Glaser, author of perhaps the most widely used assessment in critical thinking the Watson-Glaser Critical Thinking Appraisal, defines critical thinking as an attitude: "(1) an attitude of being disposed to consider in a thoughtful way the problems and subjects that come within the range of one's experience; (2) knowledge of the methods of logical enquiry and reasoning; and (3) some skill in applying those methods. Critical thinking calls for a persistent effort to examine any belief or supposed form of knowledge in the light of the evidence that supports it and the further conclusions to which it tends." Although Glaser's definition is expansive and obviously well thought out, I try to simplify critical thinking by telling clients what is needed for it to get off the ground within one's own mind. I say that critical thinking ultimately requires what I call a philosophical toolkit. This toolkit has multiple parameters suited to specific purposes in an inclusive way. Similar to how Plato and Aristotle's just agent (in Republic and Politics, respectively) only does one or two tasks and only performs that one function,these domains only serve a particular function in line with their agent's reasoning capacity. One parameter, for example, employed during critical reading involves assessing evidence based on standards. I teach my clients that there are three fundamental standards of evidence assessment: (1) relevance, (2) reasonableness, and (3) sufficiency. Glaser lists certain abilities, or skills, that underline critical thinking: "(a) to recognise problems, (b) to find workable means for meeting those problems, (c) to gather and marshal pertinent information, (d) to recognise unstated assumptions and values, (e) to comprehend and use language with accuracy, clarity and discrimination, (f) to interpret data, (g) to appraise evidence and evaluate statements, (h) to recognise the existence of logical relationships between propositions, (i) to draw warranted conclusions and generalisations, (j) to put to test the generalisations and conclusions at which one arrives, (k) to reconstruct one's patterns of beliefs on the basis of wider experience; and (l) to render accurate judgements about specfic things and qualities in everyday life." If we return to my way of stating critical thinking (i.e., which is in terms of what capacities and requisite know-how knowledge it presupposes) we might agree with M. Neil Browne and Stuart M. Keeley who argue in their Asking the Right Questions (7th ed.) that "the entire rationale for learning the steps of critical reading is to get ready to use them as a package, a cohesive assemblage of complementary abilities."
In helping students excavate the structure and form of arguments from within arguments, I always recommend a four step analytical process that goes like this. First, find the conclusion of the argument. If the client cannot find the conclusion, I ask him to submit his reasoning faculty to the "Therefore test" - which is a competency that students can master after a session with me. (Professor Alec Fisher, in his Critical Thinking (2008), spells out the "Therefore" test.) Second, give the premises entailed in the conclusion. Some of these may be assumed or implied. Third, ask yourself whether there are ambiguous items in the conclusion and/or premises. Put another way, ask yourself whether any item - be it a word, a phrase, a bracketed portion of text - could use clarification. Fourth, ask yourself what the structure of the argument is. Step four assumes that you already have a solid grasp on what argument forms look like. Most people do not have this understanding in conceptual terms - so, be sure that you can accommodate this epistemic luxury (especially because most people cannot no matter how hard they try). More or less, what this will involve is an unshakeable grasp of what constitutes a deductive argument, an inductive argument, and an argument that combines both induction and deduction. This grasp presupposes a digestion of the definitions of these multifaceted patterns of reasoning. Clients who have mastered these four steps have a knowledge that is within their working memory, accessible to their immediate awareness, ready for recall and at their cognitive disposal to detect argumentative forms effortlessly within arguments. This further presupposes an intimate acquaintence with many patterns of reasoning, including fallacies. Returning to Glaser's definition of critical thinking, we can see that his second condition requires that one have explicit knowledge, i.e., within one's working memory and accessible to one's awareness, of logical rules proper to reasoning and inquiry; this explicit knowledge is entaiiled by the above four steps.
Critical writing requires critical distance that allows you to ask yourself whether the steps in your paper add up to a coherent spelled out sum, whether the conclusions in your paper - whether these be intermediate conclusions supporting your major conclusion or not - have premises entailed in them in a coherent, cogent, spelled out way, whether the big words you use in your paper (e.g., moral realism) are defined adequately and not taken for granted, whether you have evidence that justifies your claims in a way that reflects a reasonable perspective, whether you have followed all of your instructor's guidelines throughout your paper, whether your thesis is clear and consistently carried out, and whether the supporting paragraphs aim at proving the point of your paper.
With these three types of criticality we can see that it is important to be critical. In my tutoring I stress these three elements.
20+ Expert’s sharing tips on picking the ideal math tutor
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